T. Elperin, A. Fominykh and B. Krasovitov Department of Mechanical Engineering The Pearlstone Center for Aeronautical Engineering Studies Ben-Gurion University of the Negev P.O.B. 653, Beer Sheva ISRAEL Scavenging of Soluble Radioactive Gases by Evaporating Rain Droplets from Inhomogeneous Atmosphere

Motivation and goals Fundamentals Description of the model Results and discussion Conclusions Outline of the presentation ICheaP12 Milano 2015 Ben-Gurion University of the Negev2

Gas absorption by falling droplets is the species in dissolved state Henry’s Law: Falling rain droplets Radon-222  naturally occurring, terrestrial origin Iodine-131  formed in nuclear fission Tritiated water vapor (HTO) – cosmic radiation, test of thermonuclear weapons Air Soluble Gas ICheaP12 Milano 2015 Ben-Gurion University of the Negev3

Vertical concentration gradient of soluble gases Scavenging of air pollutions Radioactive gaseous pollutants in atmosphere –Radon-222 half-life time 3.8 days –Iodine-131 half-life time 8 days –HTO half-life time 12.3 years Aircraft observation of vertical profiles of soluble trace gas concentration ICheaP12 Milano 2015 Ben-Gurion University of the Negev4

Radioactive gas absorption by droplets and rain: Booker, 1965 Atanassov & Galeriu, 2011 Dana, Wogman & Wolf, 1978 Measurements of vertical distribution of radioactive trace gases in the atmosphere: HTO – Ehhalt, 1971 Radon – Williams et al., 2011 Precipitation scavenging of gaseous pollutants by rain in inhomogeneous atmosphere: Elperin, Fominykh & Krasovitov 2015 Journ Environ Radioact Elperin, Fominykh & Krasovitov 2015 Meteorol Atm Phys Elperin, Fominykh, Krasovitov & Vikhansky 2011 Atm Environ ICheaP12 Milano 2015 Ben-Gurion University of the Negev5

Integral mass balance of the dissolved gas in a droplet: where Criteria of low gradient of concentration approach applicability (Hales 1972): (1) Concentration of the dissolved gas in a droplet : ICheaP12 Milano 2015 Ben-Gurion University of the Negev6

when I=10 mm/hour gas having low solubility when is of the order of gas having high solubility moderately soluble gas HTO methanol Velocity of temperature front propagation Velocity of scavenging front propagation Iodine-131 Rn-222 ICheaP12 Milano 2015 Ben-Gurion University of the Negev7

Since (3) Eqs (2)  (3) yield: where  volume fraction of droplets in the air. The total flux of the dissolved gas transferred by rain droplets: where u  velocity of a droplet. Total concentration of soluble gaseous pollutant in gaseous and liquid phases reads: (2) Non-evaporating droplets. Gases of low solubility ICheaP12 Milano 2015 Ben-Gurion University of the Negev8

where Using Eqs. (2) and (3) we obtain: (4) (5) (6) Equation of mass balance for soluble trace gas in the gaseous and liquid phases: Combining Eqs. (4)  (5) we obtain: wash-down front velocity is a radioactive decay constant ICheaP12 Milano 2015 Ben-Gurion University of the Negev9

Initial and boundary conditions: (7) Solution: Scavenging coefficient in isothermal atmosphere: ICheaP12 Milano 2015 Ben-Gurion University of the Negev10

where Dynamics of evaporating droplet: - coefficient of evaporation in inhomogeneous atmosphere droplet velocity droplet radius volume fraction of droplets - coefficient of evaporation in homogeneous atmosphere Evaporating droplets. Gases of high solubility ICheaP12 Milano 2015 Ben-Gurion University of the Negev11

(8) (9) (10) Equation of soluble trace gas distribution in the atmosphere: wherewash-down front velocity : Solution of Eq. (8) with the initial and boundary conditions (7) is given by the following formula ICheaP12 Milano 2015 Ben-Gurion University of the Negev12

. Fig. 1. Dependence of scavenging velocity vs. distance from a cloud bottom Fig. 2. Dependence of scavenging velocity vs. distance from a cloud bottom ICheaP12 Milano 2015 Ben-Gurion University of the Negev13

Fig. 3. Dependence of scavenging coefficient vs. rain intensity for iodine-131 Fig. 4. Evolution of HTO vapor distribution in the atmosphere caused by rain scavenging ICheaP12 Milano 2015 Ben-Gurion University of the Negev14

Fig. 5. Evolution of HTO vapor distribution in the atmosphere caused by rain scavenging Fig. 6. Dependence of scavenging coefficient vs. rain intensity for HTO vapor washout ICheaP12 Milano 2015 Ben-Gurion University of the Negev15

Fig. 7. Dependence of scavenging coefficient vs. rain intensity for NTO vapor washout Fig. 8. Dependence of scavenging coefficient vs. altitude for HTO vapor washout ICheaP12 Milano 2015 Ben-Gurion University of the Negev16

Fig. 9. Dependence of scavenging coefficient vs. altitude for HTO vapor wash out by evaporating rain droplets Fig. 10. Comparison of theoretical predictions with atmospheric measurements ICheaP12 Milano 2015 Ben-Gurion University of the Negev17

1. It is demonstrated, that if the initial altitudinal concentration distribution of a radioactive trace gas having low solubility in the atmosphere is exponential, scavenging coefficient in the region between the ground and a scavenging front is the sum of radioactive decay constant and a product of rain intensity, solubility parameter and the growth constant in the initial profile of concentration in a gaseous phase. 2. It is demonstrated that when initial temperature distribution in the atmosphere is determined by the environmental lapse, scavenging velocity is smaller than for the isothermal temperature distribution. Droplet evaporation causes further reduction of scavenging velocity. When the initial temperature distribution in the atmosphere is determined by nocturnal inversion, the competition of two factors – nocturnal inversion and droplet evaporation – leads to increase of scavenging velocity with coordinate at smaller distances from the cloud and to decrease of scavenging velocity at larger distances from the cloud. Conclusions ICheaP12 Milano 2015 Ben-Gurion University of the Negev18

3. It is demonstrated that altitudinal dependence of scavenging coefficient for radioactive soluble gas scavenging by evaporating rain droplets at different times is described either by converging or diverging lines depending on whether the altitudinal atmospheric temperature distribution is determined by the environmental lapse rate or temperature inversion. 4. The suggested model yields the same estimate of the scavenging coefficient during tritiated water vapor (HTO) washout by rain and the same dependence of the scavenging coefficient on rain intensity as the atmospheric measurements conducted by Piskunov et al. (2012). Conclusions ICheaP12 Milano 2015 Ben-Gurion University of the Negev19